Hi Mark,
You don't say how old your kids are, but unless they are 18-25 year olds who love clubbing all night, you only need to avoid the St. Julians/Paceville area, the rest of Malta and Gozo is very family friendly - you can take your kids practically everywhere.
You might like to have a look at this hotel
http://www.seabankhotel.com/main.shtml
Plenty of kids entertainment, play areas, small bowling alley etc.

It is just a short distance from the Popeye Village
http://www.popeyemalta.com/

Don't forget our buses are great fun and a very cheap way to see any of Malta's sights.

This is where I am going today
http://www.splashandfun.com.mt/

Do not forget the Dolphin Park

http://www.mediterraneo.com.mt

The Swin with the Dolphins Is Excellent Not to be Missed